Step | Hyp | Ref
| Expression |
1 | | ltexnqi 7399 |
. . . . . 6
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2 | 1 | adantl 277 |
. . . . 5
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3 | | ltrelpr 7495 |
. . . . . . . . . 10
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4 | 3 | brel 4675 |
. . . . . . . . 9
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5 | 4 | simpld 112 |
. . . . . . . 8
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P."  |
6 | | prop 7465 |
. . . . . . . . 9
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)"   |
7 | | prarloc 7493 |
. . . . . . . . 9
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8 | 6, 7 | sylan 283 |
. . . . . . . 8
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9 | 5, 8 | sylan 283 |
. . . . . . 7
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10 | 9 | ad2ant2r 509 |
. . . . . 6
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)"           |
11 | 4 | simprd 114 |
. . . . . . . . . . . . . 14
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P."  |
12 | 11 | ad2antrr 488 |
. . . . . . . . . . . . 13
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13 | 12 | ad2antrr 488 |
. . . . . . . . . . . 12
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)"   |
14 | | ltanqg 7390 |
. . . . . . . . . . . . . . . 16
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15 | 14 | adantl 277 |
. . . . . . . . . . . . . . 15
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("        |
16 | | elprnqu 7472 |
. . . . . . . . . . . . . . . . . . 19
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<."                  |
17 | 6, 16 | sylan 283 |
. . . . . . . . . . . . . . . . . 18
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18 | 5, 17 | sylan 283 |
. . . . . . . . . . . . . . . . 17
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19 | 18 | adantlr 477 |
. . . . . . . . . . . . . . . 16
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20 | 19 | ad2ant2rl 511 |
. . . . . . . . . . . . . . 15
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21 | | elprnql 7471 |
. . . . . . . . . . . . . . . . . . . 20
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<."                  |
22 | 6, 21 | sylan 283 |
. . . . . . . . . . . . . . . . . . 19
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23 | 5, 22 | sylan 283 |
. . . . . . . . . . . . . . . . . 18
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24 | 23 | adantlr 477 |
. . . . . . . . . . . . . . . . 17
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25 | 24 | ad2ant2r 509 |
. . . . . . . . . . . . . . . 16
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26 | | simplrl 535 |
. . . . . . . . . . . . . . . 16
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27 | | addclnq 7365 |
. . . . . . . . . . . . . . . 16
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28 | 25, 26, 27 | syl2anc 411 |
. . . . . . . . . . . . . . 15
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29 | | ltrelnq 7355 |
. . . . . . . . . . . . . . . . . . 19
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30 | 29 | brel 4675 |
. . . . . . . . . . . . . . . . . 18
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31 | 30 | simpld 112 |
. . . . . . . . . . . . . . . . 17
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Q."  |
32 | 31 | adantl 277 |
. . . . . . . . . . . . . . . 16
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33 | 32 | ad2antrr 488 |
. . . . . . . . . . . . . . 15
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34 | | addcomnqg 7371 |
. . . . . . . . . . . . . . . 16
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35 | 34 | adantl 277 |
. . . . . . . . . . . . . . 15
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36 | 15, 20, 28, 33, 35 | caovord2d 6038 |
. . . . . . . . . . . . . 14
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("      |
37 | | addassnqg 7372 |
. . . . . . . . . . . . . . . . 17
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("         |
38 | 25, 26, 33, 37 | syl3anc 1238 |
. . . . . . . . . . . . . . . 16
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("         |
39 | | addcomnqg 7371 |
. . . . . . . . . . . . . . . . . 18
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       |
40 | 26, 33, 39 | syl2anc 411 |
. . . . . . . . . . . . . . . . 17
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41 | 40 | oveq2d 5885 |
. . . . . . . . . . . . . . . 16
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)"   |
42 | | simplrr 536 |
. . . . . . . . . . . . . . . . 17
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43 | 42 | oveq2d 5885 |
. . . . . . . . . . . . . . . 16
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44 | 38, 41, 43 | 3eqtrd 2214 |
. . . . . . . . . . . . . . 15
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("       |
45 | 44 | breq2d 4012 |
. . . . . . . . . . . . . 14
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("     
       |
46 | 36, 45 | bitrd 188 |
. . . . . . . . . . . . 13
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       |
47 | 46 | biimpa 296 |
. . . . . . . . . . . 12
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               |
48 | | prop 7465 |
. . . . . . . . . . . . 13
              |
49 | | prloc 7481 |
. . . . . . . . . . . . 13
                                  |
50 | 48, 49 | sylan 283 |
. . . . . . . . . . . 12
                       |
51 | 13, 47, 50 | syl2anc 411 |
. . . . . . . . . . 11
    
          
                         |
52 | 51 | ex 115 |
. . . . . . . . . 10
    
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("                |
53 | 52 | anassrs 400 |
. . . . . . . . 9
    
                                    |
54 | 53 | reximdva 2579 |
. . . . . . . 8
    
    
                                     |
55 | 54 | reximdva 2579 |
. . . . . . 7
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)"                                |
56 | | prml 7467 |
. . . . . . . . . . . 12
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("          
      |
57 | | rexex 2523 |
. . . . . . . . . . . 12
     
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58 | 6, 56, 57 | 3syl 17 |
. . . . . . . . . . 11
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59 | | r19.45mv 3516 |
. . . . . . . . . . 11
                                                              |
60 | 5, 58, 59 | 3syl 17 |
. . . . . . . . . 10
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)"
 
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)"           |
61 | 60 | adantr 276 |
. . . . . . . . 9
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("                                                        |
62 | | prmu 7468 |
. . . . . . . . . . . . 13
            
      |
63 | | rexex 2523 |
. . . . . . . . . . . . 13
     

      |
64 | 6, 62, 63 | 3syl 17 |
. . . . . . . . . . . 12
 
      |
65 | | r19.43 2635 |
. . . . . . . . . . . . 13
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)"
 
                          |
66 | | r19.9rmv 3514 |
. . . . . . . . . . . . . 14
                            |
67 | 66 | orbi2d 790 |
. . . . . . . . . . . . 13
                          
 
                           |
68 | 65, 67 | bitr4id 199 |
. . . . . . . . . . . 12
                          
 
                     |
69 | 5, 64, 68 | 3syl 17 |
. . . . . . . . . . 11

                    
 
                     |
70 | 69 | rexbidv 2478 |
. . . . . . . . . 10
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                          
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71 | 70 | adantr 276 |
. . . . . . . . 9
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)"
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)"                        |
72 | | ltexprlem.1 |
. . . . . . . . . . . . . 14
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73 | 72 | ltexprlemell 7588 |
. . . . . . . . . . . . 13
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("               |
74 | 72 | ltexprlemelu 7589 |
. . . . . . . . . . . . . 14
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("               |
75 | | eleq1 2240 |
. . . . . . . . . . . . . . . . 17
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76 | | oveq1 5876 |
. . . . . . . . . . . . . . . . . 18
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77 | 76 | eleq1d 2246 |
. . . . . . . . . . . . . . . . 17
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("     
         |
78 | 75, 77 | anbi12d 473 |
. . . . . . . . . . . . . . . 16
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("                
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79 | 78 | cbvexv 1918 |
. . . . . . . . . . . . . . 15
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         |
80 | 79 | anbi2i 457 |
. . . . . . . . . . . . . 14
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       
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("               |
81 | 74, 80 | bitri 184 |
. . . . . . . . . . . . 13
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("               |
82 | 73, 81 | orbi12i 764 |
. . . . . . . . . . . 12
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)"
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           |
83 | | ibar 301 |
. . . . . . . . . . . . . . 15
        
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("                |
84 | 83 | adantr 276 |
. . . . . . . . . . . . . 14
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)"
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("                |
85 | | ibar 301 |
. . . . . . . . . . . . . . 15
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86 | 85 | adantl 277 |
. . . . . . . . . . . . . 14
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)"
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87 | 84, 86 | orbi12d 793 |
. . . . . . . . . . . . 13
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            |
88 | 30, 87 | syl 14 |
. . . . . . . . . . . 12
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("            
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               
            |
89 | 82, 88 | bitr4id 199 |
. . . . . . . . . . 11
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)"
       
                         |
90 | | df-rex 2461 |
. . . . . . . . . . . 12
                   
         |
91 | | df-rex 2461 |
. . . . . . . . . . . 12
                   
         |
92 | 90, 91 | orbi12i 764 |
. . . . . . . . . . 11
              
           
       
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("               |
93 | 89, 92 | bitr4di 198 |
. . . . . . . . . 10
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          
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                           |
94 | 93 | adantl 277 |
. . . . . . . . 9
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("          
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)"           |
95 | 61, 71, 94 | 3bitr4rd 221 |
. . . . . . . 8
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("          
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)"                        |
96 | 95 | adantr 276 |
. . . . . . 7
    
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          
                             |
97 | 55, 96 | sylibrd 169 |
. . . . . 6
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 
                          |
98 | 10, 97 | mpd 13 |
. . . . 5
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)"   |
99 | 2, 98 | rexlimddv 2599 |
. . . 4
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("            |
100 | 99 | ex 115 |
. . 3
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)"    |
101 | 100 | ralrimivw 2551 |
. 2
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)"    |
102 | 101 | ralrimivw 2551 |
1
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)"    |